Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities
Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities
复制标题
DOI：
--
复制
发表时间：
2015-04
期刊：
影响因子：
--
通讯作者：
Jing Li;Z. Xin
中科院分区：
文献类型：
--
作者：
Jing Li;Z. Xin
研究了具有退化粘性系数的正压可压缩Navier-Stokes方程整体弱解的存在性。我们构造了合适的近似系统，它具有满足能量不等式、BD熵不等式和Mellet-Vasseur型估计的光滑解。然后，在改进了Mellet-Vasseur [Comm. Partial Differential Equations 32（2007）]的紧性结果后，我们得到了具有退化粘性系数的正压可压缩Navier-Stokes方程在二维或三维周期区域或整个空间中的大初值条件下弱解的整体存在性.这特别解决了[P.L.]中的一个公开问题。狮子流体力学中的数学主题。第二卷。可压缩模型。牛津大学出版社，1998年]。
This paper concerns the existence of global weak solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients. We construct suitable approximate system which has smooth solutions satisfying the energy inequality, the BD entropy one, and the Mellet-Vasseur type estimate. Then, after adapting the compactness results due to Mellet-Vasseur [Comm. Partial Differential Equations 32 (2007)], we obtain the global existence of weak solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients in two or three dimensional periodic domains or whole space for large initial data. This, in particular, solved an open problem in [P. L. Lions. Mathematical topics in fluid mechanics. Vol. 2. Compressible models. Oxford University Press, 1998].